I have a stupid, crazy idea.
Probably won't be liked but maybe some food for thought.
Instead of creating jinchūriki and hosting the beasts indefinitely, maybe they should remain as a village summon.
What I mean by "village summon" is that the beasts return to their canonical villages (*with exceptions):
Konohagakure: KyūbiKirigakure: SanbiKumogakure: HachibiIwagakure: YonbiSunagakure: Ichibi*Exceptions:
Uzushiogakure: RokubiAmegakure: GobiOtogakure: Nanabi??:
NibiThey would exist as a protector of the village they are affiliated with but allowed to free roam. They are loved by the villagers instead of hated. They aren't mindless beasts but mentors of wisdom.
However, not everyone in the village can summon them. They must first prove their worth by trial of combat. This is done by either challenging the beast itself or the main contract holder. Should the challenger succeed in his/her match, then they are allowed to sign onto the beast's contract, no questions asked.
After a while of becoming friendly with the beast, eventually one would be given one (1) tail of chakra to seal within himself/herself as a token of the beast's affection. Could only ever activate V1 cloak and be able to utilize their distinct trademark ability to a small extent.
However, the stipulation for travelers looking to become friendly with all the beasts would be that you couldn't use the village beast to attack their own village. That would break the contract and the beast would turn on the summoner.
Could a village wage war on another village using the bijū? Probably so but they would hate every moment of it. They would be protectors of their people, not weapons of war.
The main contract holder would be the current 'Kage of the village. (S)He could also give this duty to another who is more active than they so it is entirely fair for all to achieve.
To prevent blatant bias, there would exist an OOC bijū council where those in the council take turns GM'ing different beasts.
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I do not know of what village the Nibi should go. Maybe Kusagakure, but they don't seem to be all that active any more. I don't see many Yukigakure shinobi running about either.